If the three variable lengths of a triangle are known to be three continuous natural numbers and the maximum angle is obtuse, then the lengths of the three sides are

If the three variable lengths of a triangle are known to be three continuous natural numbers and the maximum angle is obtuse, then the lengths of the three sides are

The lengths of the three sides are 2, 3 and 4
The lengths of three sides are three continuous natural numbers, so let the lengths of three sides a, B and C be n, N + 1 and N + 2 respectively. The angle of the longest side pair must be the largest angle, so the angle c must be an obtuse angle, which is obtained from the cosine theorem
cosC=(n^2+(n+1)^2-(n+2)^2)/(2n(n+1))
Angle c is obtuse, COSC

In the acute triangle ABC, the opposite sides of angles a, B and C are a, B and C respectively, and a = 2B
Find 1. The value range of angle B
2. Find the value range of a / b

1.B

In the acute triangle ABC, if the angle ＜ C = 2B ＞, what is the range of edge ＜ C ＼ B ＞?

In an acute triangle ABC, if angle c = 2 * angle B, then the range of edge C / B is?
C / (sin (angle c)) = B / (sin (angle b))
C / b = (sin (angle c)) / (sin (angle b)) = (sin (2 * angle b)) / (sin (angle b))
=(2 * sin (angle b) * cos (angle b)) / (sin (angle b))
=2 * cos (angle b)